MHT CET : Tips , Tricks and Shortcuts for Maths
Some Critical Tips : # If certain conditions are given , look for the options that satisfy the condition . # If an equation is asked then substitute the values in the option in the equation . # Use Trial and Error Method / Elimination method . # For co-ordinate geometry , draw graphs according to equations given and predict the answer . # The first step in Mathematics is mostly crucial and may require Simplification . Here are techniques of SImplifications that you should try : 1. Rationalizing 2. Plus & Minus 3. Multiplying and Dividing 4. Dividing Throughout by 5.'''Splitting the Numerator '''6. Squaring on Both Sides . Mathematical Logic Matrices # Do Adjoint first or transpose/square/other operation first , the answer is same . # Try to use the options for finding the answer , rather than solving the entire sum . # Use properties of determinants to simplify a given matrix . Trigonometric Equations # For General Solution , bring the equation in one of the sandard forms . This can be done by using factorization formulae (i.e. to convert from addition to multiplication) . # For Solutions of Triangle problems , the following techniques should be used : ## sin ## a2, b2,c2 ## A + B + C = 180 ## Half Angle ## Factorization formulae Pair of Straight Lines # Use Auxillary Equation for finding slopes . # For point of intersection of pair of lines , substitute the points in the combined equation . # For Area of triangle whose sides are given by a combined equation and equation of the third side is given , then find height by perpendicular distance formula and Area = (height)2 / √3 Vectors 3 D Geometry Lines Planes # The coefficients of x,y,z in equation of a plane ar the direction ratios of the Normal to the Plane . # The line of intersection of two planes is perpendicular to the normals of both the planes . Linear Programming Problems # Use Trial & Error Method . Continuity # If the Question is of the form 0/0 , then apply L'Hôpital's Rule Differentiation # For Implicit , use shortcut . Application of Derivatives Integration # For Indefinite Integration ; Differentiate the options to reach the Question . # For u.v ; use the shortcut # Use simplification techniques listed in point 5 of Critical Tips . Mostly , in integration , the first step is important . # For sine - cosine integrals , mostly dividing numerator and denominator with cos2x gives the answer. Definite Integration Application of Definite Integration # Draw Rough Graph for better understanding of question . # Area Shortcuts : ## Area bounded by parabola y2 = 4ax and line y = mx ; Area = 8a2/3m3 ## Area bounded by parabola x2 = 4by and line y = mx ; Area = 8b2m3/3 ## Area bounded by parabola y2 = 4ax and its latus rectum ; Area = 8a2/3 ## Area bounded by parabola x2 = 4by and its Latus Rectum ; Area = 8b2/3 ## Area bounded by parabolas y2 = 4ax and x2 = 4by ; Area = 16ab/3 Differential Equations Probability Distribution Binomial Distribution